Accurate assessment of the left ventricular (LV) systolic function is indispensable in the clinic. However, estimation of a precise index of cardiac contractility, i.e., the end-systolic elastance (Ees), is invasive and cannot be established as clinical routine. The aim of this work was to present and validate a methodology that allows for the estimation of Ees from simple and readily available non-invasive measurements. The method is based on a validated model of the cardiovascular system and non-invasive data from arm-cuff pressure and routine echocardiography to render the model patient-specific. Briefly, the algorithm first uses the measured aortic flow as model input and optimizes the properties of the arterial system model in order to achieve correct prediction of the patient's peripheral pressure. In a second step, the personalized arterial system is coupled with the cardiac model (time-varying elastance model) and the LV systolic properties, including Ees, are tuned to predict accurately the aortic flow waveform. The algorithm was validated against invasive measurements of Ees (multiple pressure-volume loop analysis) taken from n=10 heart failure patients with preserved ejection fraction and n=9 patients without heart failure. Invasive measurements of Ees (median 2.4 mmHg/mL, range [1.0, 5.0] mmHg/mL) agreed well with method predictions (nRMSE=9%, ρ=0.89, bias=-0.1 mmHg/mL and limits of agreement [-0.9, 0.6] mmHg/mL). This is a promising first step towards the development of a valuable tool that can be used by clinicians to assess systolic performance of the LV in the critically ill.